A Mathematical Odyssey

Mathematics is a poem. It is a lucid, sensual, precise exposition of beautiful ideas directed to specific goals. It is worthwhile to have as broad a cross-section of mankind as possible be conversant with what goes on in mathematics. Just as everyone knows that the Internet is a powerful and important tool for communication, so everyone should know that the Poincaré conjecture gives us important information about the shape of our universe. Just as every responsible citizen realizes that the mass-production automobile was pioneered by Henry Ford, so everyone should know that the P/NP problem has implications for security and data manipulation that will affect everyone.

This book endeavors to tell the story of the modern impact of mathematics, of its trials and triumphs and insights, in language that can be appreciated by a broad audience. It endeavors to show what mathematics means for our lives, how it impacts all of us, and what new thoughts it should cause us to entertain. It introduces new vistas of mathematical ideas and shares the excitement of new ideas freshly minted. It discusses the significance and impact of these ideas, and gives them meaning that will travel well and cause people to reconsider their place in the universe.

Mathematics is one of mankind's oldest disciplines. Along with philosophy, it has shaped the very modus of human thought. And it continues to do so. To be unaware of modern mathematics is to miss out on a large slice of life. It is to be left out of essential modern developments. We want to address this point, and do something about it. This is a book to make mathematics exciting for people of all interests and all walks of life. Mathematics is exhilarating, it is ennobling, it is uplifting, and it is fascinating. We want to show people this part of our world, and to get them to travel new paths.

• Euclidean Geometries
• RSA Encryption
• Ramsey Theory
• mathematics of finance
• relativity theory
• the four-color problem

From the book reviews:

“Most of the book requires no more than standard mathematical education and thus this book should be a must-read (opinion of reviewer) for any well-educated person, but can be also of much help for mathematicians working in education or popularization for finding new ideas or even themselves learning some not so well-known recent developments, and also it should be interesting for anybody curious what mathematics is about.” (Franka Miriam Brueckler, zbMATH, Vol. 1300, 2015)

“Krantz (Washington Univ. in St.Louis) and Parks (Oregon State Univ.) have an admirable goal: to demonstrate to uninitiated readers that mathematics is exciting and ongoing. … Complemented by an extensive index and references, the book clearly tries to make the mathematics accessible to readers willing to make the effort. … Summing Up: Recommended. Lower-division undergraduates through researchers/faculty.” (J. Johnson, Choice, Vol. 52 (4), December, 2014)

"It is clearly and invitingly written, and addresses not only some of the current issues in mathematics but also some history and some indication of the human side of the subject...it is clear to me that this book belongs in any good university library. It is also a book that should be at least looked at by any faculty member who teaches upper-level courses and has frequent contact with math majors…I certainly intend to recommend it to some of my students in the near future."

—Mark Hunacek, MAA Reviews

• Department of Mathematics, Washington University in St. Louis, St. Louis, USA

  Steven G. Krantz

• Department of Mathematics, Oregon State University, Corvalis, USA

  Harold R. Parks

Steven G. Krantz and Harold R. Parks have co-authored several classic texts including “A Primer of Real Analytic Functions, 2^nd ed.” © 2002 Birkhäuser, “The Implicit Function Theorem”, © 2003 Birkhäuser, “Geometric Integration Theory”, © 2008 Birkhäuser, “The Geometry of Domains in Space”, © 1999 Birkhäuser.  Steven Krantz’s current affiliation is Washington University in St. Louis, MO, and Harold Park’s is currently Professor Emeritus at Oregon State University, Corvalis, OR.

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